Write a third-degree polynomial in standard form with roots x = 4 and x - 2i.f(x)=a(x−4)(x−2i)(x+2i)

FobelloE

FobelloE

Answered question

2021-06-09

Write a third-degree polynomial in standard form with roots x=4 and x2i.

f(x)=a(x4)(x2i)(x+2i)

Answer & Explanation

2k1enyvp

2k1enyvp

Skilled2021-06-10Added 94 answers

By expanding,
f(x)=a(x4)(x22ix+2ix+4)
f(x)=a(x4)(x2+4)
f(x)=a[x2(x4)+4(x4)]

f(x)=a(x34x2+4x16)

Use a=1 for simplicity. A third-degree polynomial that might exist is thus:
f(x)=1(x34x2+4x16)
f(x)=x34x2+4x16

Jeffrey Jordon

Jeffrey Jordon

Expert2021-08-11Added 2605 answers

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